Finite Group Databasebeta

D4×#15691012 #38735125

order24896
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#15691012

Splittings

SylowC389 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#13095555
commutatorC2×C389C22×C8
Fitting, prime radicalC2×D4×C389C4
socleC22×C389C22×C4
cosocleC2×Dic389C23
hypercenterC2×D4#13095555
hypocenterC389C8×D4
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

1010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1575);