Finite Group Databasebeta

C2×Dic3044 #37566918

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

Aliases

direct productC2×Dic3044

Splittings

SylowC761 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D3044
commutator, cosocleC4×C761C23
FrattiniC4C22×D761
FittingC2×C8×C761C2
socle, prime radicalC22×C761D4
hypercenterC2×C8D761
hypocenterC761C2×Q16
LCSG ▷ C4×C761 ▷ C2×C761 ▷ C761
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24352

Conjugacy classes & character table

6094 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24352, 164);