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C4⋊C4×#11765849 #31995446

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

Aliases

direct productC4⋊C4×#11765849

Splittings

SylowC71 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C22×C42
FittingC2×C4×C4⋊C4×C71C2
socleC23×C71C23×C4
prime radicalC24×C71C22×C4
cosocleC22×C4×C71C24
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4⋊C4×M16
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 167562);