Finite Group Databasebeta

C22⋊C4×#13050579 #35420240

order21248
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×#13050579

Splittings

FittingC8×C22⋊C4×C83 ⋊ C2
SylowC83 ⋊ C22⋊C4×SD16

Subgroups

subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC8×C22⋊C4×C83C2
socleC23×C83C22×D4
prime radicalC23×D332C22
cosocleC22×C4×C83C24
hypercenterC8×C22⋊C4D83
hypocenterC83C22⋊C4×SD16
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ C8×C22⋊C4

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

3350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 185404);