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C25×#3861 #16814720

order3675
isoclinismisoclinic class of #3861
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×#3861

Splittings

Fitting, HallC72×C25 ⋊ C3
derived, SylowC72 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC25#3861
commutator, hypocenterC72C3×C25
FrattiniC5C5×#3861
FittingC72×C25C3
socle, cosocleC5×C72C3×C5
prime radicalC5×#3861C5
LCSG ▷ C72
UCSC1 ◁ C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 1225

A minimal faithful permutation representation — 3 generators on 39 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)(27,28,29)(30,32,31)(34,35,36)(37,39,38);(33,34,35,37,36,38,39);(26,27,28,30,29,31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofΓL(1,𝔽8)2×C25, C3×C25×#3861, C25×C22⋊#3861
maximal normal subgroup ofΓL(1,𝔽8)2×C25, C3×C25×#3861
maximal quotient ofC25×#89204, C3×C25×#3861, C25×C22⋊#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3675, 9);