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D4×Dic79⋊C4 #23766297

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×Dic79⋊C4

Splittings

SylowC79 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC2×C4×D4×C79C2
socle, cosocleC23×C79C24
prime radicalC22×D4×C79C22
hypercenterC2×C4×D4D79
hypocenterC79D4×C4⋊C4
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34306544, #34306545, #34306552, …
maximal normal subgroup of#34306544, #34306545, #34306552, …
maximal quotient ofC22⋊C4×Dic79⋊C4, C4⋊C4×Dic79⋊C4, D4×C79⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7407);