Finite Group Databasebeta

C2×#27133043 #37582936

order24448
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#27133043

Splittings

SylowC191 ⋊ C2×#494

Subgroups

subgroupG/H
centerC23C2×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×C4×C8×C191C2
socle, prime radicalC23×C191C2×D4
hypercenterC2×C4×C8D191
hypocenterC191C2×#494
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

6124 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 14926);