Finite Group Databasebeta

C2×#27133781 #37588766

order24512
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27133781

Splittings

SylowC383 ⋊ C2×M32

Subgroups

subgroupG/H
centerC2×C8C2×D383
commutatorC2×C383C22×C8
FrattiniC8C22×D383
FittingC22×C8×C383C2
socleC22×C383C2×C8
prime radicalC23×C383C8
cosocleC8×C383C23
hypercenterC22×C8D383
hypocenterC383C2×M32
LCSG ▷ C2×C383 ▷ C383
UCSC1 ◁ C2×C8 ◁ C22×C8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

6152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 964);