Finite Group Databasebeta

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C4⋊C4×#11715871 #27136199

order12352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×#11715871

Splittings

FittingC4⋊C4×C193 ⋊ C4
SylowC193 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×#11715871
commutatorC2×C193C2×C42
FittingC4⋊C4×C193C4
socleC22×C193C22×C4
prime radical, cosocleC22×D193C23
hypercenterC4⋊C4#11715871
hypocenterC193C4×C4⋊C4
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C4⋊C4

194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1489);