Finite Group Databasebeta

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C4×#17985725 #31887958

order18176
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#17985725

Splittings

SylowC71 ⋊ C4×#324

Subgroups

subgroupG/H
centerC22×C4C22⋊Dic71
commutatorC22×C71C2×C4×C8
FrattiniC23×C4C22×D71
FittingC2×C4×C4⋊C4×C71C2
socleC23×C71C2×C22⋊C4
prime radicalC24×C71C22×C4
cosocleC23×C4×C71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4×#324
LCSG ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×C4⋊C4

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

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, 60074);