Finite Group Databasebeta

C22⋊C4×#13050573 #35402032

order21248
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22⋊C4×#13050573

Splittings

FittingC8×C22⋊C4×C83 ⋊ C2
SylowC83 ⋊ C22⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D83
commutatorC22×C83C22×C42
FittingC8×C22⋊C4×C83C2
socleC23×C83C23×C4
prime radicalC24×D83C2×C4
cosocleC22×C4×C83C24
hypercenterC8×C22⋊C4D83
hypocenterC83C22⋊C4×M16
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C8×C22⋊C4

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 167196);