Finite Group Databasebeta

C22×#20259256 #37581095

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#20259256

Splittings

SylowC191 ⋊ C22×#107

Subgroups

subgroupG/H
centerC24D764
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC23×C8×C191C2
socle, prime radicalC24×C191D4
cosocleC2×C4×C191C24
hypercenterC23×C8D191
hypocenterC191C22×#107
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

6136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13085);