Finite Group Databasebeta

C4×#17985901 #31918639

order18176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C42

Aliases

direct productC4×#17985901

Splittings

FittingC2×C43×C71 ⋊ C2
SylowC71 ⋊ C4×#390

Subgroups

subgroupG/H
centerC23×C4C22×D71
commutatorC22×C71C22×C42
FrattiniC24C23×D71
FittingC2×C43×C71C2
socle, cosocleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×C43D71
hypocenterC71C4×#390
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23×C4 ◁ C2×C43

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 90755);