Finite Group Databasebeta

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C4⋊C4×#11924746 #34044555

order19072
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×#11924746

Splittings

SylowC149 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D149
commutatorC2×C149C2×C4×C8
FittingC4×C4⋊C4×C149C2
socle, prime radicalC23×C149C22×C4
cosocleC22×C4×C149C23
hypercenterC4×C4⋊C4D149
hypocenterC149C8×C4⋊C4
LCSG ▷ C2×C149 ▷ C149
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) = 19072

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 4374);