Finite Group Databasebeta

C2×#28409080 #44408340

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#28409080

Splittings

SylowC227 ⋊ C2×#430

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC22×M16×C227C2
socleC22×C227C2×C4⋊C4
prime radicalC24×C227Q8
cosocleC2×C4×C227C24
hypercenterC22×M16D227
hypocenterC227C2×#430
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

4564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13116);