Finite Group Databasebeta

C22⋊C4×D757 #37564337

order24224
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D757

Splittings

FittingC22⋊C4×C757 ⋊ C2
SylowC757 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D757
commutatorC2×C757C22×C4
FittingC22⋊C4×C757C2
socle, cosocleC22×C757C23
prime radicalC23×D757C2
hypercenterC22⋊C4D757
hypocenterC757C2×C22⋊C4
LCSG ▷ C2×C757 ▷ C757
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6056

Conjugacy classes & character table

3800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24224, 96);