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C4×#17986021 #31995351

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#17986021

Splittings

FittingC4×C4⋊C8×C71 ⋊ C2
SylowC71 ⋊ C4×#423

Subgroups

subgroupG/H
centerC2×C42C22×D71
commutatorC22×C71C22×C42
FrattiniC22×C4C23×D71
FittingC4×C4⋊C8×C71C2
socleC23×C71C23×C4
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenterC4×C4⋊C8D71
hypocenterC71C4×#423
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167467);