Finite Group Databasebeta

#367×D199 #38770628

order25472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D199

Splittings

Fitting#367×C199 ⋊ C2
SylowC199 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D199
commutatorC8×C199C22×C4
FrattiniC2×C8C22×D199
Fitting#367×C199C2
socleC22×C199C2×D8
prime radicalC22×D199D8
cosocleC2×C8×C199C23
hypercenter#367D199
hypocenterC199C2×#367
LCSG ▷ C8×C199 ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12736

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, 6288);