Finite Group Databasebeta

C2×#28409154 #44408630

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

Aliases

direct productC2×#28409154

Splittings

SylowC227 ⋊ C2×#444

Subgroups

subgroupG/H
centerC2×C4D4×D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
Fitting, prime radicalC2×#135×C227C2
socleC22×C227C4×D4
cosocleC2×C4×C227C24
hypercenterC2×#135D227
hypocenterC227C2×#444
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7264

Conjugacy classes & character table

3208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13406);