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C5×C13×Dic21 #19129673

order5460
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×Dic21
unambiguous semidirect productC3⋊(C5×C13×Dic7)
unambiguous semidirect productC7⋊(C5×Dic3×C13)

Splittings

derived, HallC3×C7 ⋊ C4×C5×C13
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ Dic7
HallC3×C5×C7 ⋊ C4×C13
HallC7×C13 ⋊ C5×Dic3
HallC3×C13 ⋊ C5×Dic7
HallC5×C7 ⋊ Dic3×C13
HallC3×C5 ⋊ C13×Dic7
SylowC7 ⋊ C5×Dic3×C13
SylowC3 ⋊ C5×C13×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D21
commutator, hypocenterC3×C7C4×C5×C13
FrattiniC2C5×C13×D21
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13×Dic63, C5×C13×C3⋊(ΓL(1,𝔽8)⋊C4), C5×C3⋊#11763961, …
maximal normal subgroup ofC5×C13×C3⋊(ΓL(1,𝔽8)⋊C4), C5×C3⋊#11763961, C5×C3⋊#11763962, …
maximal quotient ofC5×C13×Dic63, C3×C5×C13×Dic21, C5×C13×C3⋊Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 15);