Finite Group Databasebeta

C2×#27163772 #38768540

order25472
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27163772

Splittings

SylowC199 ⋊ C2×#336

Subgroups

subgroupG/H
centerC23×C4C2×D199
commutatorC2×C199C2×C4×C8
FrattiniC22×C4C22×D199
FittingC23×C8×C199C2
socle, prime radicalC24×C199C2×C4
cosocleC22×C4×C199C23
hypercenterC23×C8D199
hypocenterC199C2×#336
LCSG ▷ C2×C199 ▷ C199
UCSC1 ◁ C23×C4 ◁ C23×C8

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25472

Conjugacy classes & character table

6416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4200);