Finite Group Databasebeta

C2×#13063244 #14582879

order2752
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13063244

Splittings

SylowC43 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic43
commutatorC22×C43C22×C4
FrattiniC2×C4C22×D43
FittingC22×Q8×C43C2
socleC22×C43C22⋊C4
prime radicalC23×C43C2×C4
cosocleC2×C4×C43C23
hypercenterC22×Q8D43
hypocenterC43C2×#101
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 529);