Finite Group Databasebeta

C2×C22⋊Dic751 #37562390

order24032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic751

Splittings

SylowC751 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D751
commutatorC2×C751C22×C4
FrattiniC22C22×D751
Fitting, prime radicalC24×C751C2
socleC23×C751C22
cosocleC22×C751C23
hypercenterC24D751
hypocenterC751C2×C22⋊C4
LCSG ▷ C2×C751 ▷ C751
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12016

Conjugacy classes & character table

6020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24032, 98);