Finite Group Databasebeta

C4×C8×Dic199 #38768531

order25472
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC4×C8×Dic199

Splittings

derived, SylowC199 ⋊ C42×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C8D199
commutator, hypocenterC199C42×C8
FrattiniC22×C4C22×D199
FittingC2×C4×C8×C199C2
socle, prime radicalC23×C199C22×C4
cosocleC22×C4×C199C23
LCSG ▷ C199
UCSC1 ◁ C2×C4×C8

408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25472

Conjugacy classes & character table

6464 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4191);