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Dic1491 #20238531

order5964
automorphismAut(G) order 2504880
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic1491
unambiguous semidirect productC3⋊Dic497
unambiguous semidirect productC7⋊Dic213
unambiguous semidirect productC71⋊Dic21

Splittings

derived, HallC3×C7×C71 ⋊ C4
HallC7×C71 ⋊ Dic3
HallC3×C71 ⋊ Dic7
SylowC71 ⋊ Dic21
HallC3×C7 ⋊ Dic71
SylowC7 ⋊ Dic213
SylowC3 ⋊ Dic497

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D1491
commutator, hypocenterC3×C7×C71C4
Fitting, socleC2×C3×C7×C71C2
LCSG ▷ C3×C7×C71
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,71,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^70

Conjugacy classes & character table

1494 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic4473, C3⋊(ΓL(1,𝔽8)⋊Dic71), C3×Dic1491, …
maximal normal subgroup ofC3⋊(ΓL(1,𝔽8)⋊Dic71), C3×Dic1491, C5×Dic1491, …
maximal quotient ofDic4473, C3×Dic1491, C3⋊Dic1491, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5964, 10);