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C2×D2457 #72211549

order9828
automorphismAut(G) order 6368544
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD4914
direct productC2×D2457

Splittings

FittingC2×C7×C13×C27 ⋊ C2
derived, HallC7×C13×C27 ⋊ C22
HallC13×C27 ⋊ C2×D7
HallC7×C27 ⋊ C2×D13
HallC7×C13 ⋊ C2×D27
SylowC27 ⋊ C2×D91
SylowC13 ⋊ C2×D189
SylowC7 ⋊ C2×D351

Subgroups

subgroupG/H
center, hypercenterC2D2457
commutator, cosocle, hypocenterC7×C13×C27C22
FrattiniC9C2×D273
FittingC2×C7×C13×C27C2
socleC2×C3×C7×C13D9
LCSG ▷ C7×C13×C27
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 4914

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49);(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,36)(32,35)(33,34)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD9828, C2×D7371, C2×D12285
maximal normal subgroup ofD9828
maximal quotient ofD9828, Dic4914, C2×D7371, …

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49), (4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)(31,36)(32,35)(33,34)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44));