Finite Group Databasebeta

#344×D199 #38768590

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

Aliases

direct product#344×D199

Splittings

Fitting#344×C199 ⋊ C2
SylowC199 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D199
commutatorC22×C199C2×C42
FrattiniC22×C4C22×D199
Fitting#344×C199C2
socleC2×C199C2×#95
prime radicalC23×D199C2×C4
cosocleC22×C4×C199C23
hypercenter#344D199
hypocenterC199C2×#344
LCSG ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3184

Conjugacy classes & character table

2222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4250);