Finite Group Databasebeta

C2×Dic751⋊C4 #37562392

order24032
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×Dic751⋊C4

Splittings

SylowC751 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D751
commutatorC2×C751C22×C4
FrattiniC22C22×D751
FittingC22×C4×C751C2
socle, prime radicalC23×C751C22
cosocleC22×C751C23
hypercenterC22×C4D751
hypocenterC751C2×C4⋊C4
LCSG ▷ C2×C751 ▷ C751
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24032

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, 100);