Finite Group Databasebeta

C22×#22583550 #49134357

order36224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#22583550

Splittings

SylowC283 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D283
commutatorC2×C283C23×C8
FrattiniC8C23×D283
FittingC23×C8×C283C2
socleC23×C283C2×C8
prime radicalC24×C283C8
cosocleC8×C283C24
hypercenterC23×C8D283
hypocenterC283C22×M32
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C22×C8 ◁ C23×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18112

Conjugacy classes & character table

9104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 17606);