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Dic2037 #22550897

order8148
automorphismAut(G) order 4693248
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic2037
unambiguous semidirect productC3⋊Dic679
unambiguous semidirect productC7⋊Dic291

Splittings

derived, HallC3×C7×C97 ⋊ C4
HallC7×C97 ⋊ Dic3
HallC3×C97 ⋊ Dic7
SylowC97 ⋊ Dic21
HallC3×C7 ⋊ Dic97
SylowC7 ⋊ Dic291
SylowC3 ⋊ Dic679

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D2037
commutator, hypocenterC3×C7×C97C4
Fitting, socleC2×C3×C7×C97C2
LCSG ▷ C3×C7×C97
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,97,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^96

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic6111, C3⋊#22550908, C3⋊#22550909, …
maximal normal subgroup ofC3⋊#22550908, C3⋊#22550909, C3⋊(ΓL(1,𝔽8)⋊Dic97), …
maximal quotient ofDic6111, C3⋊Dic2037, C3×Dic2037, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8148, 12);