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C4×#17986834 #32904063

order18176
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×#17986834

Splittings

FittingC4×H(5,𝔽2)×C71 ⋊ C2
SylowC71 ⋊ C4×#585

Subgroups

subgroupG/H
centerC2×C4C24×D71
commutatorC2×C71C25×C4
FrattiniC22C25×D71
FittingC4×H(5,𝔽2)×C71C2
socle, cosocleC22×C71C26
prime radicalC2×#17986834C2
hypercenterC4×H(5,𝔽2)D71
hypocenterC71C4×#585
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076179);