Finite Group Databasebeta

C2×#28408862 #44401526

order29056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28408862

Splittings

SylowC227 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1816
commutatorC8×C227C22×C4
FrattiniC2×C8C22×D227
FittingC22×C16×C227C2
socleC22×C227#107
prime radicalC23×C227Q16
cosocleC2×C8×C227C23
hypercenterC22×C16D227
hypocenterC227C2×#368
LCSG ▷ C8×C227 ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

7276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6302);