Finite Group Databasebeta

C4×Dic1522 #37566866

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

Aliases

direct productC4×Dic1522

Splittings

SylowC761 ⋊ C4×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D761
commutatorC2×C761C22×C4
FrattiniC22C22×D761
FittingC42×C761C2
socle, prime radical, cosocleC22×C761C23
hypercenterC42D761
hypocenterC761C4×Q8
LCSG ▷ C2×C761 ▷ C761
UCSC1 ◁ C2×C4 ◁ C42

70 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, 112);