Finite Group Databasebeta

← Prev (#22555073) Next (#22555075) →

Dic2121 #22555074

order8484
automorphismAut(G) order 5090400
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic2121
unambiguous semidirect productC3⋊Dic707
unambiguous semidirect productC7⋊Dic303

Splittings

derived, HallC3×C7×C101 ⋊ C4
HallC7×C101 ⋊ Dic3
HallC3×C101 ⋊ Dic7
SylowC101 ⋊ Dic21
HallC3×C7 ⋊ Dic101
SylowC7 ⋊ Dic303
SylowC3 ⋊ Dic707

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D2121
commutator, hypocenterC3×C7×C101C4
Fitting, socleC2×C3×C7×C101C2
LCSG ▷ C3×C7×C101
UCSC1 ◁ C2

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,7,101,2|a^2=e,b^a=b^2,c^a=c^6,d^a=d^100

Conjugacy classes & character table

2124 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofDic6363, C3⋊(ΓL(1,𝔽8)⋊Dic101), C3⋊Dic2121, …
maximal normal subgroup ofC3⋊(ΓL(1,𝔽8)⋊Dic101), C3×Dic2121, Dic4242
maximal quotient ofDic6363, C3⋊Dic2121, C3×Dic2121, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8484, 9);