Finite Group Databasebeta

D8×Dic383 #37588434

order24512
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic383

Splittings

SylowC383 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D383
commutatorC4×C383C22×C4
FrattiniC2×C4C22×D383
Fitting, prime radicalC2×D8×C383C2
socleC22×C383C2×D4
cosocleC2×C4×C383C23
hypercenterC2×D8D383
hypocenterC383C4×D8
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

2702 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 632);