Finite Group Databasebeta

C2×C4⋊Dic761 #37566855

order24352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic761

Splittings

SylowC761 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D761
commutatorC2×C761C22×C4
FrattiniC22C22×D761
FittingC22×C4×C761C2
socle, prime radicalC23×C761C22
cosocleC22×C761C23
hypercenterC22×C4D761
hypocenterC761C2×C4⋊C4
LCSG ▷ C2×C761 ▷ C761
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24352

Conjugacy classes & character table

6100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 101);