Finite Group Databasebeta

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C32×C72×D5 #17984401

order4410
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C32×C72 · Schur multiplier (H2) = C3×C7

Aliases

direct productC32×C72×D5
unambiguous semidirect productC5⋊(C2×C32×C72)

Splittings

Fitting, socle, HallC32×C5×C72 ⋊ C2
derived, SylowC5 ⋊ C2×C32×C72
HallC5×C72 ⋊ C2×C32
HallC32×C5 ⋊ C2×C72

Subgroups

subgroupG/H
center, hypercenterC32×C72D5
commutator, cosocle, hypocenterC5C2×C32×C72
FrattiniC1G
Fitting, socleC32×C5×C72C2
LCSG ▷ C5
UCSC1 ◁ C32×C72

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 2205

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3)(7,8,9,10,11,12,13)(21,22,23,24,25);(4,5,6)(14,15,16,17,18,19,20)(22,25)(23,24)

Conjugacy classes & character table

1764 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C72×D25, C32×C5×C72×D5, C32×C72×C5⋊D5
maximal normal subgroup ofC32×C5×C72×D5
maximal quotient ofC32×C72×D25, C32×C5×C72×D5, C32×C72×C5⋊D5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4410, 122);