Finite Group Databasebeta

C2×#27132690 #37581079

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27132690

Splittings

SylowC191 ⋊ C2×#424

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#117×C191C2
socleC23×C191C22×C4
prime radicalC24×C191C2×C4
cosocleC2×C4×C191C24
hypercenterC2×#117D191
hypocenterC191C2×#424
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×#117

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13069);