Finite Group Databasebeta

#102×Dic199 #38768667

order25472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct product#102×Dic199

Splittings

SylowC199 ⋊ C4×#102

Subgroups

subgroupG/H
centerC23D4×D199
commutatorC4×C199C2×C42
FrattiniC22×C4C22×D199
FittingC2×#102×C199C2
socleC23×C199C2×D4
prime radicalC22×D4×C199C22
cosocleC22×C4×C199C23
hypercenterC2×#102D199
hypocenterC199C4×#102
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12736

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, 4327);