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C22×C4×#11924078 #34037189

order18752
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#11924078
unambiguous semidirect productD293⋊(C2×C42)

Splittings

FittingC22×C4×C293 ⋊ C4
derived, SylowC293 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#11924078
commutator, hypocenterC293C22×C42
FrattiniC2C23×#11924078
FittingC22×C4×C293C4
socleC23×C293C2×C4
prime radicalC23×D293C22
cosocleC2×D293C24
LCSG ▷ C293
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#95×#11924078, C4×(C2×#11924078)⋊C4, #49173960, …
maximal normal subgroup of#95×#11924078, C4×(C2×#11924078)⋊C4, #49173960, …
maximal quotient ofC2×C42×#11924078, C22×(C2×#11924078)⋊C4, C2×#34037065, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 1609);