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C52⋊#3862 #16814729

order3675
automorphism?
homologyAbelianization (H1) = C3 · Schur multiplier (H2) = C5×C7

Aliases

unambiguous semidirect productC52⋊#3862

Splittings

Fitting, socle, derived, HallC52×C72 ⋊ C3
SylowC72 ⋊ C52⋊C3
SylowC52 ⋊ #3862

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C72C3
LCSG ▷ C52×C72
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 105

Polycyclic presentation:

3,5^2,7^2|b^a=bc^2,c^a=bc^3,d^a=d^2,e^a=e^4

Conjugacy classes & character table

411 conjugacy classes — view the full character table.

Relationships

derived subgroup of#20301286⋊C3, C3×#20301286
maximal subgroup ofC52⋊C3×#3862, ΓL(1,𝔽8)×C7⋊(C52⋊C3), #3861⋊(C52⋊C3), …
maximal normal subgroup ofC52⋊C3×#3862, ΓL(1,𝔽8)×C7⋊(C52⋊C3), #3861⋊(C52⋊C3), …
maximal quotient ofC52⋊#89205, C3×C52⋊#3862, C22⋊(C52⋊#3862)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3675, 18);