Finite Group Databasebeta

C2×#27132531 #37574910

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

Aliases

direct productC2×#27132531

Splittings

SylowC191 ⋊ C2×#383

Subgroups

subgroupG/H
centerC24C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC22×C42×C191C2
socle, prime radicalC24×C191C23
cosocleC23×C191C24
hypercenterC22×C42D191
hypocenterC191C2×#383
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C24 ◁ C22×C42

624 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, 6900);