Finite Group Databasebeta

C2×#27132438 #37574109

order24448
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27132438

Splittings

SylowC191 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D191
commutatorC2×C191C2×C4×C8
FrattiniC2×C8C22×D191
FittingC22×C16×C191C2
socle, prime radicalC23×C191C2×C8
cosocleC2×C8×C191C23
hypercenterC22×C16D191
hypocenterC191C2×#346
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C22×C8 ◁ C22×C16

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

6160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6099);