Finite Group Databasebeta

C2×#27163793 #38770439

order25472
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27163793

Splittings

SylowC199 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D199
commutatorC2×C199C2×C4×C8
FrattiniC2×C8C22×D199
FittingC22×C16×C199C2
socle, prime radicalC23×C199C2×C8
cosocleC2×C8×C199C23
hypercenterC22×C16D199
hypocenterC199C2×#346
LCSG ▷ C2×C199 ▷ C199
UCSC1 ◁ C22×C8 ◁ C22×C16

200 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, 6099);