Finite Group Databasebeta

C2×#27133777 #37588397

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

Aliases

direct productC2×#27133777

Splittings

SylowC383 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1532
commutatorC4×C383C22×C4
FrattiniC2×C4C22×D383
FittingC22×C8×C383C2
socleC22×C383C4⋊C4
prime radicalC23×C383Q8
cosocleC2×C4×C383C23
hypercenterC22×C8D383
hypocenterC383C2×#108
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12256

Conjugacy classes & character table

6140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 595);