Finite Group Databasebeta

C2×#27133848 #37589114

order24512
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27133848

Splittings

SylowC383 ⋊ C2×#131

Subgroups

subgroupG/H
centerC2×C4C22×D383
commutatorC2×C383C23×C4
FrattiniC4C23×D383
Fitting, prime radicalC2×#41×C383C2
socleC22×C383C22×C4
cosocleC4×C383C24
hypercenterC2×#41D383
hypocenterC383C2×#131
LCSG ▷ C2×C383 ▷ C383
UCSC1 ◁ C2×C4 ◁ C2×#41

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

3860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 1312);