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C43×#1039⋊C3 #27166380

order12900
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C43 · Schur multiplier (H2) = C5

Aliases

direct productC43×#1039⋊C3
unambiguous semidirect product#1039⋊(C3×C43)

Splittings

derived, SylowC52 ⋊ C3×C4×C43
HallC43×#1039 ⋊ C3
HallC43×C52⋊C3 ⋊ C4
HallC52×C43 ⋊ C3×C4
Hall#1039 ⋊ C3×C43
HallC52⋊C3 ⋊ C4×C43

Subgroups

subgroupG/H
center, hypercenterC2×C43(C5⋊D5)⋊C3
commutator, hypocenterC52C3×C4×C43
FrattiniC2C43×(C5⋊D5)⋊C3
Fitting, socleC2×C52×C43C2×C3
prime radicalC2×C43×C52⋊C3C2
cosocleC2×C52C2×C3×C43
LCSG ▷ C52
UCSC1 ◁ C2×C43

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 2580

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,4)(3,6,10,7,5,12)(8,13,15,14,11,9)(16,19,18,17)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(1,3,8,14,7)(2,5,11,13,6)(4,9,10,12,15)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12900, 49);