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SL(2,𝔽3)×C25 #10597033

order600
isoclinismisoclinic class of SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productSL(2,𝔽3)×C25
unambiguous semidirect productQ8⋊(C3×C25)
unambiguous semidirect product(Q8×C25)⋊C3

Splittings

Fitting, HallQ8×C25 ⋊ C3
derived, SylowQ8 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25A4
commutator, hypocenterQ8C3×C25
Frattini, socleC2×C5C5×A4
FittingQ8×C25C3
prime radicalC5×SL(2,𝔽3)C5
cosocleC5×Q8C3×C5
LCSG ▷ Q8
UCSC1 ◁ C2×C25

21 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC25⋊#226, C25⋊GL(2,𝔽3)
maximal subgroup ofC25×#226, C25×GL(2,𝔽3), C25⋊#226, …
maximal normal subgroup ofC25×#226, C25×GL(2,𝔽3), C25⋊#226, …
maximal quotient ofC2×SL(2,𝔽3)×C25, C25×Q8⋊C9, C3×SL(2,𝔽3)×C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(600, 14);