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C52×#379 #13103116

order1600
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C22×C4×C52 · Schur multiplier (H2) = C26×C5

Aliases

direct productC52×#379

Subgroups

subgroupG/H
center, socleC23×C52C23
commutatorC22C22×C4×C52
Frattini, cosocleC23C23×C52
prime radicalC25×C52C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C52 ◁ G

2024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 400

A minimal faithful permutation representation — 3 generators on 22 points:

(1,2,3,4,5)(12,14)(15,16,17,18)(20,22);(6,7,8,9,10)(19,20)(21,22);(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC5⋊D5×#379, #379×#1043, #72258509
maximal subgroup ofC5⋊D5×#379, #72258509, C52×#2846
maximal normal subgroup ofC5⋊D5×#379, #72258509, C52×#2846

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 5468);