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C25×GL(2,𝔽3) #11924887

order1200
isoclinismisoclinic class of #226
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×GL(2,𝔽3)

Splittings

FittingQ8×C25 ⋊ D3
derivedSL(2,𝔽3) ⋊ C2×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25S4
commutator, hypocenterSL(2,𝔽3)C2×C25
Frattini, socleC2×C5C5×S4
FittingQ8×C25D3
prime radicalC5×GL(2,𝔽3)C5
cosocleC5×SL(2,𝔽3)C2×C5
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,33,28,29,32,31,30);(27,30,33)(28,31,32)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 97);