Finite Group Databasebeta

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C4×#17985765 #31902654

order18176
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#17985765

Splittings

SylowC71 ⋊ C4×#342

Subgroups

subgroupG/H
centerC22×C4(C2×D71)⋊C4
commutatorC22×C71C43
FrattiniC25C22×D71
FittingC2×C4×C22⋊C4×C71C2
socleC23×C71C2×C22⋊C4
prime radical, cosocleC25×C71C23
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C4×#342
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 74770);