Finite Group Databasebeta

C22×#19127548 #35562576

order21248
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#19127548

Splittings

FittingC22×#95×C83 ⋊ C2
SylowC83 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC25C22×D83
commutatorC2×C83C23×C42
FrattiniC23C24×D83
FittingC22×#95×C83C2
socleC25×C83C23
prime radicalC25×D83C22
cosocleC23×C83C25
hypercenterC22×#95D83
hypocenterC83C22×C4×C22⋊C4
LCSG ▷ C2×C83 ▷ C83
UCSC1 ◁ C25 ◁ C22×#95

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10624

Conjugacy classes & character table

3440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 327740);