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C2×D5957 #37558582

order23828
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD11914
direct productC2×D5957
unambiguous semidirect product(C2×C7)⋊D851
unambiguous semidirect product(C2×C23)⋊D259
unambiguous semidirect product(C2×C37)⋊D161

Splittings

Fitting, socleC2×C7×C23×C37 ⋊ C2
derived, HallC7×C23×C37 ⋊ C22
HallC23×C37 ⋊ C2×D7
HallC7×C37 ⋊ C2×D23
HallC7×C23 ⋊ C2×D37
SylowC37 ⋊ C2×D161
SylowC23 ⋊ C2×D259
SylowC7 ⋊ C2×D851

Subgroups

subgroupG/H
center, hypercenterC2D5957
commutator, cosocle, hypocenterC7×C23×C37C22
FrattiniC1G
Fitting, socleC2×C7×C23×C37C2
LCSG ▷ C7×C23×C37
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 11914

A minimal faithful permutation representation — 2 generators on 69 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69);(4,9)(5,8)(6,7)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

5960 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD23828
maximal normal subgroup ofD23828
maximal quotient ofDic11914, D23828

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23828, 27);