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Dic5×#63270 #19129693

order5460
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productDic5×#63270

Splittings

derived, HallC5×C7×C13 ⋊ C3×C4
HallC7×C13×Dic5 ⋊ C3
HallC5×#63270 ⋊ C4
HallC13×Dic5 ⋊ ΓL(1,𝔽8)
HallC7×Dic5 ⋊ C13⋊C3
HallC7×C13 ⋊ C3×Dic5
HallC5×C13 ⋊ C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C13⋊C3
SylowC13 ⋊ Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ Dic5×C13⋊C3
SylowC5 ⋊ C4×#63270

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×#63270
commutator, hypocenterC5×C7×C13C3×C4
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

264 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×Dic5×#63270, Dic15×#63270, …
maximal normal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×Dic5×#63270, C5×Dic5×#63270, …
maximal quotient ofDic5×#11717941, C3×Dic5×#63270, Dic15×#63270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 35);