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D476 #11745768

order952
automorphismAut(G) order 91392
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD476
unambiguous semidirect productC4⋊D119

Splittings

FittingC4×C7×C17 ⋊ C2
HallC7×C17 ⋊ D4
SylowC17 ⋊ D28
SylowC7 ⋊ D68

Subgroups

subgroupG/H
center, FrattiniC2C2×D119
commutator, socle, cosocleC2×C7×C17C22
FittingC4×C7×C17C2
hypercenterC4D119
hypocenterC7×C17D4
LCSG ▷ C2×C7×C17 ▷ C7×C17
UCSC1 ◁ C2 ◁ C4

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 476

A minimal faithful permutation representation — 2 generators on 28 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);(2,4)(6,11)(7,10)(8,9)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

2^3,7,17|b^2=c,b^a=bc,d^a=d^6,e^a=e^16

Conjugacy classes & character table

241 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14274031, #14274032, #14274036, …
maximal normal subgroup of#14274031, #14274032, #14274036, …
maximal quotient of#14274083, D952, Dic476, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(952, 26);