Finite Group Databasebeta

C22×C4⋊Dic43 #14583350

order2752
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊Dic43

Splittings

SylowC43 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D43
commutatorC2×C43C23×C4
FrattiniC22C23×D43
FittingC23×C4×C43C2
socle, prime radicalC24×C43C22
cosocleC22×C43C24
hypercenterC23×C4D43
hypocenterC43C22×C4⋊C4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1000);