Finite Group Databasebeta

C2×#27160909 #38744504

order25216
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27160909

Splittings

SylowC197 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1576
commutatorC8×C197C22×C4
FrattiniC2×C8C22×D197
FittingC22×C16×C197C2
socleC22×C197#107
prime radicalC23×C197Q16
cosocleC2×C8×C197C23
hypercenterC22×C16D197
hypocenterC197C2×#368
LCSG ▷ C8×C197 ▷ C4×C197 ▷ C2×C197 ▷ C197
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

6316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 6302);