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C4⋊C4×#14523339 #45664184

order32896
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×#14523339

Splittings

SylowC257 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D257
commutatorC2×C257C2×C4×C8
FittingC4×C4⋊C4×C257C2
socle, prime radicalC23×C257C22×C4
cosocleC22×C4×C257C23
hypercenterC4×C4⋊C4D257
hypocenterC257C8×C4⋊C4
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

296 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 181 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) = 32896

Conjugacy classes & character table

5200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 4374);