Finite Group Databasebeta

C2×#27163848 #38770642

order25472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27163848

Splittings

SylowC199 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1592
commutatorC8×C199C22×C4
FrattiniC2×C8C22×D199
FittingC22×C16×C199C2
socleC22×C199#107
prime radicalC23×C199Q16
cosocleC2×C8×C199C23
hypercenterC22×C16D199
hypocenterC199C2×#368
LCSG ▷ C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12736

Conjugacy classes & character table

6380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 6302);