Finite Group Databasebeta

#339×D199 #38768554

order25472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D199

Splittings

Fitting#339×C199 ⋊ C2
SylowC199 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D199
commutatorC4×C199C2×C42
FrattiniC22×C4C22×D199
Fitting#339×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC23×D199D4
cosocleC22×C4×C199C23
hypercenter#339D199
hypocenterC199C2×#339
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3184

Conjugacy classes & character table

2828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4214);