Finite Group Databasebeta

C22×C4⋊(C227⋊C8) #44408285

order29056
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊(C227⋊C8)

Splittings

SylowC227 ⋊ C22×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4C2×D227
commutatorC2×C227C23×C8
FrattiniC2×C4C23×D227
FittingC22×C42×C227C2
socle, prime radicalC24×C227C2×C4
cosocleC2×C4×C227C24
hypercenterC22×C42D227
hypocenterC227C22×C4⋊C8
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C23×C4 ◁ C22×C42

640 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 469 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

Conjugacy classes & character table

7312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 13061);