Finite Group Databasebeta

C22×#17985726 #31963793

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#17985726

Splittings

FittingC22×C4⋊C8×C71 ⋊ C2
SylowC71 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D71
commutatorC4×C71C23×C8
FrattiniC42C23×D71
FittingC22×C4⋊C8×C71C2
socleC24×C71C22⋊C4
prime radicalC23×D284C4
cosocleC42×C71C24
hypercenterC22×C4⋊C8D71
hypocenterC71C22×D4⋊C8
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

1886 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, 135909);