Finite Group Databasebeta

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H(3,ℤ/4)×Dic83 #35309567

order21248
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C2×C43

Aliases

direct productH(3,ℤ/4)×Dic83

Splittings

SylowC83 ⋊ C4×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C42×D83
commutatorC4×C83C43
FrattiniC23×C4C22×D83
FittingC2×H(3,ℤ/4)×C83C2
socleC22×C83C2×#95
prime radicalC24×C83C2×D4
cosocleC23×C4×C83C23
hypercenterC2×H(3,ℤ/4)D83
hypocenterC83C4×H(3,ℤ/4)
LCSG ▷ C4×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

954 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5312

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 74731);