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Dic2163 #22575739

order8652
automorphismAut(G) order 5295024
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic2163
unambiguous semidirect productC3⋊Dic721
unambiguous semidirect productC7⋊Dic309
unambiguous semidirect productC103⋊Dic21

Splittings

derived, HallC3×C7×C103 ⋊ C4
HallC7×C103 ⋊ Dic3
HallC3×C103 ⋊ Dic7
SylowC103 ⋊ Dic21
HallC3×C7 ⋊ Dic103
SylowC7 ⋊ Dic309
SylowC3 ⋊ Dic721

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D2163
commutator, hypocenterC3×C7×C103C4
Fitting, socleC2×C3×C7×C103C2
LCSG ▷ C3×C7×C103
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,103,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^102

Conjugacy classes & character table

2166 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic6489, C3⋊#22575751, C3⋊#22575750, …
maximal normal subgroup ofC3⋊#22575751, C3⋊#22575750, C3⋊(ΓL(1,𝔽8)⋊Dic103), …
maximal quotient ofDic6489, C3⋊Dic2163, C3×Dic2163, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 12);