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Dic1351 #19129238

order5404
automorphismAut(G) order 3112704
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic1351
unambiguous semidirect productC7⋊Dic193

Splittings

derived, HallC7×C193 ⋊ C4
SylowC193 ⋊ Dic7
SylowC7 ⋊ Dic193

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D1351
commutator, hypocenterC7×C193C4
Fitting, socleC2×C7×C193C2
LCSG ▷ C7×C193
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,7,193,2|a^2=d,b^a=b^6,c^a=c^192

Conjugacy classes & character table

1354 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic1351, Dic4053, #30633858, …
maximal normal subgroup ofC3×Dic1351, #30633858, ΓL(1,𝔽8)⋊Dic193, …
maximal quotient ofC3×Dic1351, Dic4053, C5×Dic1351, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5404, 4);