Finite Group Databasebeta

C2×#27133785 #37588775

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

Aliases

direct productC2×#27133785

Splittings

SylowC383 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#20259442
commutator, cosocleC8×C383C23
FrattiniC8C22×D383
Fitting, prime radicalC2×D8×C383C2
socleC22×C383D8
hypercenterC2×D8D383
hypocenterC383C2×SD32
LCSG ▷ C8×C383 ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

2696 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 973);