Finite Group Databasebeta

C4×#17985889 #31918615

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

Aliases

direct productC4×#17985889

Splittings

FittingC2×C4×C4⋊C4×C71 ⋊ C2
SylowC71 ⋊ C4×#388

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C4×#388
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

2134 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, 90731);