Finite Group Databasebeta

C2×#27132493 #37574312

order24448
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27132493

Splittings

SylowC191 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1528
commutatorC8×C191C22×C4
FrattiniC2×C8C22×D191
FittingC22×C16×C191C2
socleC22×C191#107
prime radicalC23×C191Q16
cosocleC2×C8×C191C23
hypercenterC22×C16D191
hypocenterC191C2×#368
LCSG ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

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, 6302);