Finite Group Databasebeta

C2×#13063260 #14582944

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

Aliases

direct productC2×#13063260

Splittings

SylowC43 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D43
commutatorC4×C43C22×C4
FrattiniC2×C4C22×D43
FittingC2×M16×C43C2
socleC22×C43C4⋊C4
prime radicalC23×C43Q8
cosocleC2×C4×C43C23
hypercenterC2×M16D43
hypocenterC43C2×#108
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 594);