Finite Group Databasebeta

D8×C22⋊Dic71 #32013276

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD8×C22⋊Dic71

Splittings

SylowC71 ⋊ C22⋊C4×D8

Subgroups

subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC23×D8×C71C2
socleC23×C71C22×D4
cosocleC22×C4×C71C24
hypercenterC23×D8D71
hypocenterC71C22⋊C4×D8
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 185392);