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C42×#11924078 #34037063

order18752
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C43

Aliases

direct productC42×#11924078

Splittings

FittingC42×C293 ⋊ C4
derived, SylowC293 ⋊ C43

Subgroups

subgroupG/H
center, hypercenterC42#11924078
commutator, hypocenterC293C43
FrattiniC22C22×#11924078
FittingC42×C293C4
socleC22×C293C22×C4
prime radical, cosocleC22×D293C23
LCSG ▷ C293
UCSC1 ◁ C42

258 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#49173612, C4×C8×#11924078, #97×#11924078, …
maximal normal subgroup of#49173612, C4×C8×#11924078, #97×#11924078, …
maximal quotient of#95×#11924078, C4×(C2×#11924078)⋊C4, C4×C8×#11924078, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 1483);