Finite Group Databasebeta

C4×#20300318 #44408551

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

Aliases

direct productC4×#20300318

Splittings

SylowC227 ⋊ C4×#137

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D227
commutatorC4×C227C23×C4
FrattiniC2×C4C23×D227
FittingC4×#41×C227C2
socleC22×C227C22×D4
prime radicalC2×#41×C227C22
cosocleC2×C4×C227C24
hypercenterC4×#41D227
hypocenterC227C4×#137
LCSG ▷ C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

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, 13327);